BMS1031 Lecture 5: Principles of Biomechanics

Learning Outcomes

• Examples of Forces & Effects: Understand and recognize how forces, as vectors, combine.

• Newton’s Laws: Apply and show how Newton's 1st, 2nd, and 3rd laws apply to simple cases.

• Torque Calculation: Calculate torque using the formula: Torque (τ) = Force (F) × Perpendicular Distance (d) from the axis.

• Rotational Equilibrium: Explain muscle and lever action examples and recognize lever systems in the body.

Forces

• Force Defined: Interaction between two objects, which can either be a push (compression) or pull (tension).

• Unit of Force: The SI unit for force is Newton (N), defined as 1 N = 1 kg m/s².

• Vector Nature: Forces are vectors; they can be represented with free-body diagrams and add vectorially.

• Effect of Forces: Forces cause changes in motion resulting from acceleration.

Gravity, Weight, and Mass

• Gravity: The force of gravity acting on an object; objects near Earth's surface experience approximately 9.8 N of downward force per kg (Fᵍ = mg).

• Weight: The magnitude of gravitational force acting on an object, commonly confused with mass (often measured in kg).

Balanced Forces - Equilibrium

• Equilibrium: For an object to be in equilibrium, the net force must be zero; equal forces acting in opposite directions lead to a net force of zero.

  • Example: A tendon under tension, equal tension forces at each end yield a net force of zero.

Newton’s Laws of Motion

1. 1st Law (Inertia): An object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by an external force.

2. 2nd Law (F = ma): The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

3. 3rd Law (Action-Reaction): For every action, there is an equal and opposite reaction.

Torque & Lever Systems

• Torque Defined: Torque (or moment of force) is defined as τ = L × F, where L is the perpendicular distance from the pivot point to the line of action of the force.

• Units of Torque: Torque is measured in Newton-meters (N·m).

• Rotational Equilibrium: An object in rotational equilibrium will have zero net torque (Στ = 0).

Center of Mass

• The center of mass is the point in an object that represents the average position of all its mass; it follows the path of translational motion, even while rotating.

Examples of Torque Application

1. Balanced Torques: For balance on a seesaw, the torque exerted by each child must be equal around the pivot point.

2. Muscle Action: Example includes muscles acting at an angle to provide necessary torque to balance gravitational forces acting on limbs.

Lever Classifications in the Human Body

1. 1st Class Levers: Fulcrum is between the load and the effort (e.g., neck muscles supporting the head).

2. 2nd Class Levers: Load is between the fulcrum and the effort (e.g., calf muscles lifting the heel).

3. 3rd Class Levers: Effort is between the fulcrum and the load (e.g., bicep muscle flexing the forearm).